There has been considerable effort expended in developing tools for the nondestructive analysis of materials. This interest is particularly strong in the integrated circuit industry. In the prior art, techniques were developed where high powered optical microscopes are used to analyze surface characteristics of a sample Subsurface features have been analyzed through the use of acoustic waves that are generated in the sample and interact with the elastic features beneath the surface of the sample. More recently, a new branch of investigations has developed wherein thermal waves are used to derive information about thermal features in a sample.
In a thermal wave system, a localized periodic heating is induced at the surface of the sample Energy from the heat source is absorbed by the sample at or near its surface and a periodic surface heating occurs at the modulation frequency of the heat source. This periodic surface heating is the source of thermal waves that propagate from the heated region. The thermal waves interact with thermal boundaries and barriers in a manner that is mathematically equivalent to scattering and reflection of conventional propagating waves. Thus, any features on or beneath the surface of the sample that have thermal characteristics different from their surroundings will reflect and scatter thermal waves and thus become visible to these thermal waves. Thermal waves can be induced in a wide variety of sample materials and can be used to detect these thermal features. Thermal waves, however, are critically damped and travel only about one thermal wavelength thus the penetration range is quite limited.
The subject invention is directed to a new and improved nondestructive analytical tool which in some respects is quite analogous to systems which perform thermal wave analyses In the subject invention, the density variations of a diffusing electron-hole plasma are monitored to yield information about features in a semiconductor.
As is well known, semiconductors have a band gap between the valence and conduction bands. Input energy is needed to raise an electron from the valence band to the conduction band which results in the creation of an electron-hole pair. Typically the input energy to the system will exceed the band gap energy and the electron will be excited from the valance band to an energy level above the conduction band. These electron carriers will, in a relatively short period of time (.tau..congruent.10.sup.-13 seconds) , give up a portion of their energy to the lattice through nonradiative transitions to the unoccupied states near the bottom of the conduction band. After a much longer time (.tau.=10.sup.-3 to 10.sup.-8 seconds) these carriers will give up the remainder of their energy to the lattice by recombining with the holes of the valence band. Prior to this recombination, there exists a plasma of electrons and holes whose spatial density is governed by diffusion in a manner analogous to the flow of heat from a thermal source.
If an evaluation is made of this plasma diffusion, information can be derived about the composition and lattice structure of a semiconductor. In some situations, where the plasma is generated in a periodic fashion, "plasma waves" can be generated and information about subsurface features can be derived using an analysis similar to a thermal wave analysis.
Changes in plasma density will result in a change in the index of refraction at the surface of a sample. This dependance has been reported by D. H. Auston et. al., in "Picosecond Ellipsometry of Transient Electron-Hole Plasmas in Germanium" (Physical Review Letters, Vol 32, No. 20, May 20, 1974). This paper reports that changes in the index of refraction, due to the variations in plasma density, can be detected by reflecting a probe beam off the surface of the sample within the area which has been excited. (See also "Picosecond Time-Resolved Plasma and Temperature-Induced Changes of Reflectivity and Transmission in Silicon," J. M. Liu, et. al., Applied Physics Letters Vol. 41 No. 7 Oct. 1, 1982). These preliminary articles were merely attempting to analyze how the plasma moves through a sample. No effort was made to analyze the sample itself through the interaction of the plasma with the sample. Furthermore, the energy source was not modulated, that is, a periodic plasma was not generated, and thus would prevent an analysis similar to that described in the subject invention.
When the energy source is modulated and a periodic plasma is generated, the probe beam, which is reflected off the surface of the sample, will undergo periodic changes in both intensity and phase. Changes in intensity can be measured by a relatively simple photodetector technique. Changes in phase can be measured through monitoring by interferometry techniques or by monitoring the periodic angular displacements of a probe beam.
Very recently, some attempts have been made to analyze the plasma through its affects on acoustic waves generated in a silicon sample (See "Effect of Photocarriers on Acoustic Wave Propagation for Measuring Excess Carrier Density and Lifetimes in Silicon", Stearns, et. al., Applied Physics Letters, Vol. 45 No. 11, Dec. 1, 1984). In the experimental arrangement reported in this article, the energy source was modulated and a periodic plasma was generated. However, there was no attempt made to analyze the sample itself through interactions of the plasma with the sample. Furthermore, the analytical tool described in the latter article was a contact technique requiring an acoustic transducer.
In order to detect optical changes in the index of refraction it is necessary that the probe beam be located within the periodically excited area. The periodically excited area can be defined in terms of a radius with the center point being the center of the energy source as follows: ##EQU1## where r.sub.o is the radius of the energy source and u is the distance over which the plasma will diffuse in the sample. In the situation where the decay time .tau. (the time it takes for the electron-hole pairs to recombine) is relatively short compared to the modulation period 1/.omega., where .omega. is the modulation frequency in radians/second, (i.e., .omega..pi. is less than 1) then the diffusion length (u) of the plasma is given by the following equation: EQU u=(D.tau.).sup.1/2 ( 2)
where D is the diffusivity of the plasma.
A more interesting situation occurs when the decay time .tau. is long compared to the period of the modulation of the energy beam (i.e., .omega..tau. is greater than 1) In this case, "plasma waves" will be created and u is given by the following equation: EQU u=(2D/.omega.).sup.1/2 ( 3)
These "plasma waves" are critically damped and can be analyzed in a manner directly analogous to thermal waves. More specifically, in this limiting case, the plasma diffusion length u depends on the modulation frequency .omega. and can therefore be varied by changing the modulation frequency. Information about the subsurface region as a function of depth beneath the sample surface is obtained by studying the periodic changes in the probe beam when the modulation frequency of the energy source is varied. This analysis is directly analogous to the studies described in detail in copending U.S. patent application Ser. No. 389,623 filed on June 18, 1982, and now U.S. Pat. No. 4,513,384, issued Apr. 23, 1985 assigned to the same assignee as the subject invention and incorporated herein by reference.
The analysis described in the latter patent application is intended to give information as to either layer thickness or compositional variables of a sample as a function of depth. These techniques can be applied with the method of the subject invention when the decay time .tau. is long compared to the period of modulation of the energy beam
As described above, there are many important and significant similarities between thermal wave analysis and plasma density analysis, which is the subject of this application. There are also important differences. Most importantly, electron-hole plasma analysis is limited to semiconductor materials. However, when semiconductor analysis is desired, this technique provides some advantages over a thermal wave analysis. For example, plasma density analysis can be significantly more sensitive than a thermal wave analysis. Thermal wave studies only provide information as to thermal features plasma density analysis, which can be thought of as an analysis of the movement of highly interactive electrons, will provide information on a wide variety of changes in the structure and composition of a semiconductor sample. Furthermore, experiments have shown that the sensitivity of the plasma to variations in some sample characteristics can be anywhere from 10 to 100 times greater than that which would be expected from a thermal wave interaction alone.
Another distinguishing feature of this system is that unlike a thermal wave approach, a periodic heat source is not required. As pointed out above, in order to do a thermal wave analysis, it is necessary to induce a periodic localized heating on the sample surface to generate thermal waves. In the subject system, all that is required is a periodic energy source which will interact and excite electrons from the valance band to the conduction band. In practice, the means for exciting the plasma will be similar to those commonly used in generating thermal waves. However, it should be understood that the generation of heat is not required, and that it is only necessary to impart enough energy to the electrons to overcome the band gap in the sample. If this energy is carefully controlled, no localized heating will occur.
Another difference between the subject approach and thermal wave systems is that despite the fact that the energy beam is modulated, a "plasma wave" will not always be generated. As pointed out above, if the period of the modulated energy beam is greater than the recombinant or decay time (.tau.), no plasma waves will be created In contrast, if the modulation frequency (.omega.) is controlled such that the period between cycles is less than the decay time (.tau.), plasma waves will be created.
For many measurement situations, a wavelike phenomenon, such as the plasma wave, is unnecessary for evaluation. For example, and as discussed in detail in the specification, applications which do not require depth profiling or the analysis of sample variations as a function of depth, do not require the generation of plasma waves. However, in applications where sample variations as a function of depth need to be studied, it is necessary to generate and study plasma waves.
Therefore, it is an object of the subject invention to provide a new and improved method and apparatus for evaluating surface and subsurface conditions in a semiconductor sample.
It is a further object of the subject invention to provide a new and improved method and apparatus for analyzing semiconductors wherein a sample is excited in a manner to create an electron-hole plasma.
It is another object of the subject invention to provide a method and apparatus wherein features in a semiconductor are anaylzed by generating an electronhole plasma in the sample and monitoring the diffusion of this plasma using a radiation probe.
It is a further object of the subject invention to provide a method and apparatus for evaluating surface and subsurface conditions in a semiconductor sample wherein changes in a reflected probe beam are monitored to study the density variations of the electron-hole plasma.